The central ray in CT scanning systems is the projection of the centre-of-rotation on the detector. The central ray must be a known parameter for all reconstruction algorithms. Any error in the central ray generally leads to artifacts and distortion in the reconstructed images which sometimes are very difficult to identify. The current conventional methods used for central ray determination are discussed.
A conventional method is by using a fixed position. Like many medical check X-ray CT, the centre of rotation is always fixed and usually only needs to be calibrated once a year, for example. For this system, because a resolution of about several millimeters is acceptable, there is no high accuracy requirement about the central ray. The use of a fixed centre of rotation is only applicable to medical X-ray CT system because micro-CT systems for industry applications typically need to adjust the magnification and scanning position of the object according to the size, shape of the object and the requirement for different resolution.
FIG. 1A illustrates a conventional system 110 for determining central ray utilizing a wire phantom 116. FIG. 1A illustrates a conventional method of a wire phantom that is scanned first to generate a sinogram of the wire from which the central ray can be determined. A wire phantom is actually a small straight wire fixed at the centre of a plastic tube. The wire is made of heavy metal such as tungsten. It must be small enough so that it can be treated as a point to meet the requirement for certain accuracy. With the wire phantom method, before scanning the object, the wire phantom is scanned first for a whole round at the same place used for scanning the object. The sinogram of the projection data of the wire phantom is used to determine the central ray. In the system 110, a source 112 is projecting a projection beam 114 towards the wire phantom 116 and detected by a digital detector 120. A manipulator and rotator 122 rotate the wire phantom about a rotation of axis 118. FIG. 1A illustrates the situation where a wire phantom is scanned and FIG. 1B is a typical sinogram 130 of this scan. Calibration with a wire phantom is currently a common practice in many existing commercially available systems. However, this method requires one more scanning which greatly slows down the whole inspection process and reduces the effective lifetime of the system for real applications. It also presents significant calibration error in high-magnification scanning due to the mechanical movement involved.
FIG. 2 illustrates another conventional approach that uses a look-up table 140. A look-up table is actually a relationship between the central ray and the scanning position. It is usually established by scanning a calibration unit such as a wire phantom with the rotation axis placed at different positions. Once a lookup table is created, the central ray in a particular scan is read from the look up table according to the actual object position. Using a lookup table is straightforward but in practice this is simply not reliable because of the high requirement for the accuracy and repeatability of the manipulation system. Considering the large area of movement and multiple movement degrees of freedom, the look up table approach is only used for low-accuracy or low-resolution inspection applications. For some micro-CT system for industry applications, a lookup table about the relationship between the central ray and the scanning physical position is pre-calibrated and created.
FIG. 3A illustrates another conventional approach 150 using a geometrical relationship of the scanning. This method makes use of the property that during the scanning the boundary of the sinogram is generated always by the point that has the longest distance to the centre of rotation. With the knowledge of the central channel 162, the central ray 164 may be unambiguously determined from the left and right boundary points 158,160, in accordance with relationship between the object rotation axis 152 and the two tangential points 154,156. FIG. 3B shows a sinogram and boundary detection 170 obtained with this method. The geometrical method has been proven to be an effective method which eliminates the need for extra scan and is able to provide a comparable accuracy to other methods such as calibrating with a wire phantom. However, this method generally only works with a normal scan which requires an object to be fully covered in the X-ray fan beam. Besides, this method encounters a certain difficulty if large fluctuation in X-ray intensity occurs during the scanning process or poor image contrast is observed around the two boundary points.
In a conventional method such as the universal method as shown in FIG. 4A-C, a flowchart (FIG. 4A) and graphs (FIGS. 4B and 4C) of a conventional method is shown for determining the central ray by measuring the mismatching level of two CT images reconstructed for one slice respectively with part of the projection data. FIG. 4A shows a typical flow chart of this method with a two-step strategy, that is, a rough search round with a large search range and a large search step followed by a fine search round with a small search range and a small search step. This method performs two reconstructions for one slice respectively with 1-180 views and 181-360 views over a set of assumed central ray values and measures the mismatching level of the two reconstructed images for each assumed central ray. The central ray value that corresponds to the minimum of the measurement in the fine search round will be determined as the best estimate to the real central ray. FIG. 4B and FIG. 4C show respectively the typical search results 54,56 in the rough search round and the fine search round. A slice is first reconstructed with half of the projections (1-180 views), then reconstructed with another half of the projections (181-360 views) over a set of assumed central rays, measuring the mismatching level of the two reconstructed images by performing an subtraction-square-sum operation between them, and identifying the real central ray as the one corresponding to the minimum of the measurement. This method is an automated method that does not require any prior calibration for scanning an object at any positions within the X-ray beam. The universal method has an accuracy at least as good as the wire phantom method, much better than the lookup table method, and more reliable and robust than the geometrical method which relies on the accurate detection of the boundary information of the sinogram. The main problem of the universal central ray method is that it is still thought as too slow for future in-situ application or high-throughput inspection. The universal method involves iterative reconstructions of one slice over a set of assumed central ray values within a search range defined 38. With each assumed central ray in the search range, the sinogram needs to go through the processes of the fan-beam to parallel-beam conversion 38, forward and Inverse Fourier transform 39, and two reconstructions, one with 1-180 views 40 and one with 181-360 views 42. The determination time is mainly determined by the reconstruction size, the step size and the search range defined. Among all the processes, the Fourier transform and the reconstruction 44 take about more than 90% of the total time required. For example, if a two-step search strategy is used, which typically involves about 40 cycles, a program written in Matlab would take about 20 minutes to complete the whole process with a reconstruction size of 200×200. A two-step strategy means one rough search 46 with a large search range and a large search step size is followed by a fine search 48 with a small search range and a small step size. If using a program written in C++, this may reduce to about 4 minutes.
There is thus a need for a system and method that alleviates the problems associated with the above universal central ray determination procedures. There is a need for an automated and fast method and algorithm that can directly determine the central ray with the fan-beam projection data of the object to be scanned. There is a need for a reliable and robust central ray determination method which is insensitive to intensity variation of the X-ray. There is a need for a measurement method for the quality of the reconstructed images in computed tomography (CT).